bayesian modeling using the mcmc procedure：使用mcmc方法的贝叶斯建模.pdf

Paper 257-2009 Bayesian Modeling Using the MCMC Procedure Fang Chen, SAS Institute Inc, Cary, NC ABSTRACT Bayesian methods have e increasingly popular in modern statistical analysis and are being applied to a broad spectrum of scienti?c ?elds and research areas. This paper introduces the new MCMC procedure in SAS/STAT , which is designed for general-purpose putations. The MCMCprocedure enables you to carry out analysis on a wide range plex Bayesian statistical models. The procedure uses the Markov chain Monte Carlo (MCMC) algorithm to draw samples from an arbitrary posterior distribution, which is de?ned by the prior distributions for the parameters and the likelihood function for the data that you specify. This paper describes how to use the MCMC procedure for estimation, inference, and prediction. INTRODUCTION This paper introduces the new MCMC procedure in SAS/STAT ?software. The MCMC procedure is currently available for SAS as an experimental procedure and will e production during 2009. The MCMC procedure is based on Markov chain Monte Carlo methods; it performs posterior sampling and statistical inference for Bayesian parametric models. The procedure ?ts single-level or multilevel models. These models can take various forms, from linear to nonlinear models, by using standard or nonstandard distributions. To use the procedure, you declare parameters in the model and specify prior distributions of the parameters and a conditional distribution for the response variable given the parameters. The MCMC procedure enables you to ?t models by using either a keyword for a standard form (normal, binomial, gamma) or SAS programming statements to specify a general distribution. The MCMC procedure uses a random walk Metropolis algorithm to simulate samples from the model you specify. You can also choose an optimization technique (such as the quasi-Newton algorithm) to estimate the posterior mode and approximate the covariance matrix around the mode. The putes a number